Looking Beyond the Magnitude of Impedance to Phase
The second effect of high ESR is that it causes a phase shift away from
the expected ideal of 90 degrees between voltage and current at all
frequencies.
Some designers assume that if the resonant frequency is high compared to the frequency of interest, all will be well  the capacitor can be used up to the natural selfresonant frequency or, when the capacitor maker does not give that information, as high a frequency as possible as long as the impedance curve remains fairly linear in appearance. This is not a valid assumption for many capacitor applications, however. It can be true for powersupply bypassing, but for many circuit applications, the useful frequency range of the capacitor is limited by its phase response rather than its impedance. The phase response is degraded well below the capacitor's natural or selfresonant frequency when series losses are added. These losses may arise from the construction of the capacitor itself, or they may arise externally, usually from wire or cable losses and the driving source impedance.
Phase Response
In Figures 2 and 3, we show that filter circuits (e.g., loudspeaker
crossovers, RIM equalization, D/A filters, etc.} cannot be thoroughly
designed without integrating the actual, measured incircuit
performance of the capacitors (and inductors as well) into the overall
system design.
Figure 2 shows the phase/magnitude of a 4.4 mfd/1OOv bipolar electrolytic capacitor. The capacitor itself has a resonance at 450 kHz with 1inch lead length, which looks as if it is well out of the audible range. But because of the capacitor's high ESR, phase was down 5 degrees to 85 at only 4.0 kHz and  10 degrees at 14 kHz. When this capacitor was measured incircuit (with 12 inches of circuit wire), the phase had degraded from 89 degrees at 100 Hz to  85 at approximately 800 Hz, and  55 degrees at 10 kHz! If this designer had doubled the lead length from the capacitor to the load, phase would have begun to sour at a very low frequency, even though the resonance would still be at a relatively high frequency!
MlT's filmandfoil type MultiCap^{TM}, with its very low losses, has superior phase characteristics all the way out to its natural resonance. With this capacitor, designers will find fewer differences between their theory and the actual practice than with inferior capacitors. Less fudging and tweaking of the network component values will be needed to make the design "look right"  such adjustments at best give only a compromised performance.
Audible Effects
When capacitors do not maintain a 90degree current phase relationship to voltage at the frequency of interest
land for a couple of octaves beyond), proper musicsignal summation becomes difficult to achieve. Image blurring
and ambience retrieval suffer. And the relationships of harmonics to fundamental will be altered.
For those who strive to produce the best possible performance, only the most linear and ideal capacitors can be acceptable.

